49.16.4 problem 1(d)

Internal problem ID [7702]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 4. Linear equations with Regular Singular Points. Page 149
Problem number : 1(d)
Date solved : Wednesday, March 05, 2025 at 04:50:48 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-5 x y^{\prime }+9 y&=x^{2} \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-5*x*diff(y(x),x)+9*y(x) = x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2} \left (\ln \left (x \right ) c_{1} x +c_{2} x +1\right ) \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]-5*x*D[y[x],x]+9*y[x]==x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (c_1 x+3 c_2 x \log (x)+1) \]

✓ Sympy. Time used: 0.254 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - x**2 - 5*x*Derivative(y(x), x) + 9*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = x^{2} \left (C_{1} x + C_{2} x \log {\left (x \right )} + 1\right ) \]